00:01
Hello, let's have a look on the question.
00:02
So it is given to us that n is following negative binomial and having values r is equal to 15 and p is equal to 1 upon 5 which is equal to 0 .2.
00:19
So therefore the expectation of negative binomial is given by r divided by p which is equal to 15 multiplied by 1 upon 5, 1 upon 1 upon 5.
00:33
So this will be equal to 15 into 5.
00:36
This value is equal to 75.
00:38
Next we need to find out the variance of n.
00:41
Variance of n is equal to r multiplied by 1 minus p divided by p 2.
00:51
So this value is equal to r is 15 multiplied by 0 .8 divided by 0 .22.
00:59
So this value is equal to 300.
01:01
Now the claim amounts for the claim amount for claim amount it is given that x is equal to u10 this is following uniform distribution having parameters 0 and 10 so expectation of x is given by 10 by 2 which is equal to 5 variance of x will be given by 10 minus 0 multiply by 2 divided by 12 so this value is equal to 100 divided by well.
01:37
Now using compound distribution formula, using the compound distribution formula, we can write expectation of s is equal to expectation of n multiplied by expectation of x...